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Hindawi Publishing CorporationJournal of Computer Networks and CommunicationsVolume 2012, Article ID 259824, 13 pagesdoi:10.1155/2012/259824

Research Article

Learning-Based Spectrum Sensing for Cognitive Radio Systems

Yasmin Hassan, Mohamed El-Tarhuni, and Khaled Assaleh

Department of Electrical Engineering, American University of Sharjah, P.O. Box 26666, Sharjah, UAE

Correspondence should be addressed to Mohamed El-Tarhuni, [email protected]

Received 27 June 2012; Revised 4 November 2012; Accepted 26 November 2012

Academic Editor: Lixin Gao

Copyright © 2012 Yasmin Hassan et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper presents a novel pattern recognition approach to spectrum sensing in collaborative cognitive radio systems. In theproposed scheme, discriminative features from the received signal are extracted at each node and used by a classifier at a centralnode to make a global decision about the availability of spectrum holes for use by the cognitive radio network. Specifically, linearand polynomial classifiers are proposed with energy, cyclostationary, or coherent features. Simulation results in terms of detectionand false alarm probabilities of all proposed schemes are presented. It is concluded that cyclostationary-based schemes are themost reliable in terms of detecting primary users in the spectrum, however, at the expense of a longer sensing time compared tocoherent based schemes. Results show that the performance is improved by having more users collaborating in providing featuresto the classifier. It is also shown that, in this spectrum sensing application, a linear classifier has a comparable performance to asecond-order polynomial classifier and hence provides a better choice due to its simplicity. Finally, the impact of the observationwindow on the detection performance is presented.

1. Introduction

In the past few years, there have been remarkable develop-ments in wireless communications technology leading to arapid growth in wireless applications. However, this dramaticincrease in wireless applications is severely limited by band-width scarcity. Traditionally, fixed spectrum assignments, inwhich frequency bands are statically assigned to licensedusers are employed. The static spectrum allocation preventsfrom assigning vacant spectrum bands to new users andservices. Further, spectrum occupancy measurements haveshown that some licensed bands are significantly underuti-lized. For example, the Spectral Policy Task Force reportedthat radio channels are typically occupied 15% of the time[1]. Hence, the limitation in the available spectrum bandsoccurs mainly due the underutilization of available spectrumresulting from the inefficient static allocation techniques.This underutilization of available spectrum resources hasled regulatory bodies to urge the development of dynamicspectrum allocation paradigms, called cognitive radio (CR)networks.

A CR network senses the operating environment forvacant spectrum opportunities and dynamically utilize theavailable radio resources [2, 3]. In CR technology, unlicensed

(secondary) users are allowed to share the spectrum origi-nally assigned to licensed (primary) users. Hence, frequencybands that are legally assigned to primary users are exploitedby secondary users when primary users are idle. However,primary users have the right to occupy their assigned bandswhenever needed. Consequently, secondary users should beaware of the variations in the surrounding environmentand should be ready to adjust their operating parametersaccordingly in order to make a productive usage of thespectrum [4].

Secondary users in CR networks are restrained by thecondition of providing adequate protection to primary users.Hence, secondary users need to employ efficient spectrumsensing techniques that ensure the quality of service forprimary users and exploit all dynamic spectrum sharingchances. That is to say, in order to facilitate dynamicspectrum access in licensed bands, effective spectrum sensingalgorithms need to be developed whereby high reliabilityalong with efficient utilization is achieved.

Spectrum sensing approaches that are commonly consid-ered in CR applications include energy detection, cyclosta-tionary feature detection, and coherent detection [2, 4–6].Based on the prior knowledge a secondary user has about

2 Journal of Computer Networks and Communications

primary users, a specific technique would be more appro-priate. For instance, if a priori information about a primaryuser signal is known by secondary users, coherent detectioncan be utilized. Coherent detection uses features such assynchronization messages, pilots, preambles, midambles,and spectrum spreading sequences. When these patternsare known at the CR network, sensing is performed bycorrelating the incoming signal with the known patterns [6].Coherent sensing based on pilot detection was implementedexperimentally in [7]. On the other hand, when CRs havevery limited information about the primary signal, energydetection is used. Another reason for using energy detectionin spectrum sensing applications is the low complexityinvolved. However, the performance of energy detection interms of the ability to detect primary signals is degraded,especially in low signal-to-noise ratio (SNR) conditions.

Another approach to spectrum sensing is based oncyclostationary detection to sense the presence of a primaryuser by exploiting cyclostationary features exhibited by thestatistics of the primary signal [8]. In cyclostationary detec-tion, the spectral correlation function (SCF) of a modulatedsignal is analyzed to decide on the presence of primary signalin the target spectrum. Cyclostationary feature detectionbased on multicycle detection has been proposed in [9,10], where the cyclostationarity is detected at multiplesof the cycle frequency. In orthogonal frequency divisionmultiplexing (OFDM) systems, a cyclic prefix is intentionallyinserted as a guard interval, which could be used to detectcyclostationarity of incumbent primary signals [11, 12].Furthermore, the OFDM waveform could be modified inorder to generate specific signatures at certain frequencies[13] such that the cyclic features created by these signaturesare then extracted via cyclostationary detection to achieve aneffective signal identification mechanism.

In order to preserve the quality of service for primaryusers, the interference caused by secondary users needs tobe maintained below an acceptable level. Hence, reliablespectrum sensing needs to be performed by secondary usersto detect the presence of a primary user, especially undershadowing and fading effects. Collaboration among spatiallydisplaced secondary users is, hence, required to mitigate sucheffects without requiring excessively long detection times. Inthis case, several CR nodes utilize the spatial diversity gainprovided by cooperative spectrum sensing to achieve betterperformance in fading environments [4, 9, 10, 14, 15].

In this work, we propose a collaborative spectrumsensing approach in CR applications. Specifically, we uti-lize classification techniques used in pattern recognitionapplications to identify the available and busy bands in theradio spectrum. Previously, pattern recognition techniqueswere used mainly in signal classification for determiningtype of modulation rather than spectrum sensing [16–18]. The proposed pattern recognition scheme represents acentralized cooperative CR network, whereby the decisionof spectrum availability is made at a central node aftercollecting spectral sensing information from all collaboratingusers. Sensing information is subjected to a classifier modelthat outputs a global decision regarding the availabilityof the target spectrum band. Polynomial classifiers are

proposed in this work as classifier models, in which first- andsecond-order expansions are investigated. Three spectrumsensing techniques are implemented to provide informativefeatures to the classifier about the surrounding environment.Spectrum sensing techniques used for feature extractioncan be classified into parametric and nonparametric. Non-parametric detection includes energy detection where thecognitive network does not have a priori knowledge on theprimary users’ signals. On the other hand, in parametricdetection, cyclic features characterizing primary signals andprior knowledge of synchronizing preamble patterns areutilized. The parametric detection schemes include coherentdetection and cyclostationary feature detection.

Many of the collaboration techniques in the prior workimplement maximum ratio combining, likelihood ratio test,or hard decision rules, such as AND logic operation andone-out-of-n rule [4, 5, 19, 20]. Cooperative sensing basedon energy detection has been proposed in [4], in whichlinear combination of local test statistics from multipleusers is utilized in the decision making. The performanceof a cyclostationary-based spectrum sensing cooperative CRsystem was considered in [20, 21], where binary decisionswith different fusion rules of the secondary user’s decisionsusing cyclic detectors were compared. Moreover, multipleuser single-cycle detectors are proposed to accommodatesecondary user collaboration [9], where different cyclicfrequencies are utilized by different users and combined tomake a global decision. In [10], the summation of localtests statistics of secondary users is employed as the fusionrule when multicycle detection is performed by CRs. Finally,cooperation based on hard decision rules was investigatedwith coherent detection in [7].

The contributions of this paper are as follows. Theproblem of collaborative spectrum sensing in CR networks isinvestigated from a new perspective based on a pattern recog-nition approach. More specifically, polynomial classifiers areused in this work. The design, validation and evaluation offirst- and second-order polynomial classifiers are presented.The parameters of these classifiers are optimized basedon the signal strength of the individual secondary usersin a collaborative manner. The performance in terms offalse alarm rate and detection probability under low SNRconditions has been thoroughly examined and analyzed.Comprehensive performance evaluation of energy-baseddetection is provided. Finally, extensive simulations areperformed to evaluate the performance of the proposedclassifiers with parametric spectrum sensing schemes, wherecarrier frequency and synchronization preamble patterns areassumed to be known at the CR network. The results of thisinvestigation were partially presented in [22, 23].

The rest of the paper is organized as follows: in Section 2,we introduce the signal model and the proposed cooperativespectrum sensing scheme. In Section 3, different featureextracting techniques are presented. The polynomial classi-fier structure is developed in Section 4. Simulation resultsand discussions are given in Section 5. Finally, Section 6concludes the paper. All notations and symbols used in thispaper are explained in Table 1.

Journal of Computer Networks and Communications 3

Table 1: List of notations.

Notation/symbol Explanation

rj[n] Received signal by user j

x[n] Transmitted primary signal

gj Channel gain coefficients

ηj[n] Zero-mean additive white Gaussian noise (AWGN) at user j’s end

N Number of users in cognitive network

d N-dimensional feature vector consisting of features extracted from different CRs

M Number of samples observed to make a decision (observation window size)

Rαx(τ) Cyclic autocorrelation function

Sαx[k] Spectral correlation density function

Rjc[k] Cross-correlation between the received signal and the preamble sequence

ϕ(d) l-dimensional vector consisting of the monomials of a another vector d

wi The classifier model parameters for class i

DtrainK ×N matrix, where N is the dimensionality of the input feature vectors (provided by N CR users)and K is the number of feature vectors used in the training process

M A (K × l) matrix representing the polynomial expansion of elements in training data set Dtrain

ti An ideal target vector representing the ideal channel state (ON or OFF)

Yd Binary global decision on channel availability

2. Signal Model and System Description

We consider dynamic spectrum allocation in a collaborativeCR network with the structure illustrated in Figure 1. Theprimary user and CR network are assumed to coexist withinthe same geographical area. The CR network consists ofN users with a central node that detects the presence ofprimary signals and decides on the channel availability.CRs temporarily access the underutilized licensed frequencybands, without conflict with primary spectrum holders’usage.

The binary hypothesis test for spectrum sensing isformulated as

r j[n] ={gjx [n] + ηj[n] : H1

ηj[n] : H0for j = 1, 2, . . . ,N , (1)

where r j[n] represents the received signal by the jth CR userat the nth instant of time, and x[n] denotes the primary usertransmitted signal. H1 represents the hypothesis of an occu-pied spectrum, while H0 corresponds to an idle spectrum.The received signal at the jth user is corrupted by a zero-mean additive white Gaussian noise (AWGN), ηj[n] withvariance σj2. The primary signal passes through a wirelesschannel to reach the jth CR user with a channel gain gj .The wireless channel is modeled as a flat channel with slowfading. Each channel has a complex valued coefficient withRayleigh distributed magnitude and uniformly distributedphase over the range [0, 2π). The channel coefficients ofdifferent CRs in the network are assumed to be constant overa number of received signal symbols, that is, slow fading,and are also assumed to be independent and identicallydistributed.

In this paper, spectrum sensing in CR networks isformulated as a pattern recognition problem. Generallyspeaking, pattern recognition is used to classify a given set ofdata into several different categories. A pattern recognitionsystem assigns an input signal to one of a number ofknown categories based on features derived to emphasizecommonalities between those signals. A generic term thatis used to describe input signals that need to be classifiedin a recognition system is patterns. Usually, patterns maynot be useful for classification, and hence they need tobe processed to acquire more useful input to the classifier[24, 25]. This processed information is called features. Insupervised learning, a labeled training set of feature vectors isprocessed through the classification algorithm to determinethe classifier model parameters. These parameters are usedin predicting the class of new data that have not beenseen during the learning phase. In this paper, supervisedpattern recognition is utilized at the CR base station (CRBS)to classify available spectrum holes such that maximumdetection is achieved with a desired false alarm rate.

In the proposed system, secondary users are constantlysensing the target spectrum band for primary signal pres-ence. Within a secondary user receiver, discriminative fea-tures are extracted from the sensed signal. The extractedfeatures from the difference secondary users are transmittedto the CRBS through a relatively low data rate control chan-nel. This control channel is used for exchanging informationbetween CRs and CRBS. At the CRBS, a decision about thespectrum availability is made based on a pattern recognitionclassifier that is previously trained. The block diagram ofthe proposed system is depicted in Figure 2 showing thesignal flow of the CR inputs through feature extraction


Primary network Cognitive radio network

TVROTVRO

TVRO

TVROgroup

Centernode

Main stationTV broadcaster

Satellite

Figure 1: An example of a centralized CR network.

CRBS: polynomial expansion and classification

Decision logic:

Feature extraction

Feature extraction

CR1 CRN

d1 dN

xNx1

H0 or H1

yi ≶ λ

· · ·

Figure 2: Pattern recognition CR system model.

and classification leading to a decision about the spectrumavailability at the CRBS.

The first step is spectrum sensing which involves inputdata acquisition by processing the signals received byantennas at different CR receivers. The received signalof the jth user is assumed to follow the mathematicalmodel described in (1). These signals are transformedinto multidimensional feature vectors that compactlycharacterize the sensed signals.

When secondary users in a CR network have noprior information about the transmitted primary signal,the energy of the received signal is used at the featureextraction stage and utilized by the classifier to discriminatebetween the noise only and primary signal present cases.On the other hand, if prior information, such as carrierfrequency and synchronizing patterns, is known about theprimary user’s signal, feature extraction will be achievedby either exploiting cyclic features present in the signal orthrough coherent detection. Features extracted by any of thementioned detection schemes will exhibit certain patternswhen the spectrum is occupied by a primary user thatare different from the patterns extracted when only noiseis present in the spectrum. The difference between thesepatterns will be exploited as discriminative input data to

the pretrained classifier for decision making. The followingsection discusses the different feature extraction schemesused in this paper.

3. Feature Extraction Techniques

In this work, three different feature extraction schemeshave been used, namely, noncoherent energy-based features,cyclostationary-based features, and coherent detection-basedfeatures.

3.1. Energy-Based Feature Extraction. Energy detection isone of the most commonly used techniques in spectrumsensing due to its low computational complexity and simpleimplementation. It does not require any prior knowledgeof the primary users’ signal; hence, it is considered as anonparametric detection scheme. The classification systemidentifies spectrum availability relying on the energy of thereceived signal over an observation period. However, the taskof detecting the signal becomes very challenging under lowSNR levels and fading channels [5, 14]. As a preprocessingstep, the received signal by the jth secondary user, r j(t),which follows the model specified in (1), is filtered accordingto the desired frequency band to obtain yj(t). The sampled


Frequency smoothing over P frequency bins

e−iπαn

e+iπαn

U[K]u(n)

V∗[k]

S αx [k]xj[n] = [x1 · · · xM]

M-point

FFT

M-point

FFT

v(n)(·)∗

Figure 3: Cyclostationary feature detection estimator.

version of the signal is used to extract one representativeenergy feature dj defined as

dj = 1M

M∑n=1

∣∣∣yj[n]∣∣∣2

, (2)

where M is the length of the observation period in samples.Accordingly, a feature vector for this observation periodis constructed from the N users’ signals such as d =[d1 · · ·dN ]T , where T is the vector transpose operation.This feature vector will be presented to the classifier in theclassification stage. A new set of energy features is obtainedevery observation window.

3.2. Cyclostationary-Based Feature Extraction. Most commu-nication signals can be modeled as cyclostationary ran-dom processes, as they are usually characterized by built-in periodicities in their mean and autocorrelation. Theseunderlying periodicities arise from the use of sinusoidalcarriers, repeating spreading codes, pulse trains, or cyclicprefixes in signal transmission. On the other hand, noisesignals do not exhibit such periodicity characteristics. Hence,the sensing of the spectrum availability can be based on thedetection of the signal periodicity.

A binary phase shift keying (BPSK) that digitally mod-ulated signal x(t) with symbol duration T0 has a cyclicautocorrelation function (CAF) defined as

Rαx(τ) � 1

T0

∫ T0/2

−T0/2

(x(t +

τ

2

)x∗(t − τ

2

)e− j2παt

)dt, (3)

where τ is a nonzero delay, and α ∈ {0,±1/ T0,±2/ T0, . . .}.Rαx(τ) represents the Fourier transform of the delay

product x(t + τ/2)x∗(t− τ/2) evaluated at the frequencies inα. The signal x(t) is said to contain second order periodicityif and only if the Fourier transform of Rα

x(τ) has discretespectral lines at nonzero frequencies α /= 0 [26, 27].

Cyclostationarity of a signal leads to the presence ofspecific patterns in the spectrum of the signal, which canbe examined using the so-called spectral correlation density

function (SCD) [27, 28] defined as the Fourier transform ofits CAF as

Sαx(f ;α) =

∫∞−∞

Rαx(τ)e− j2π f τdτ. (4)

The SCD is the cross-correlation function between thespectral translates of the signal at f ± α/2, for some cyclicfrequency α. This function is smoothed using a frequencysmoothing vector (window) W with P frequency bins. Sincediscrete-time samples of the received are used in estimatingthe SCD, it is possible to show that the SCD is given by

Sαx[k] = 1P

(P−1)/2∑v=−(P−1)/2

X[k +

α

2+ v]X∗[k − α

2+ v]W(v),

(5)

with

X[k] =M−1∑n=0

x[n]e− j2πkn/M , (6)

where k = 0, 1, . . . ,M − 1, and M is the number of samplesover which the spectrum of the received signal is calculated(FFT length). The SCD estimation is implemented to obtainthe cyclic feature extraction receiver structure as shown inFigure 3. The SCD of the received signal will depend onthe presence or absence of the primary transmitted signalaccording to the following:

Sα0r j [k] =

⎧⎪⎪⎨⎪⎪⎩∣∣∣gj∣∣∣2

Sα0x [k] + Sα0

ηj [k] : H1,

Sα0ηj [k] : H0,

(7)

where Sα0ηj [k] is the SCD of the AWGN only at the jth

CR user, and Sα0x [k] is the SCD of the transmitted primary

signal at some cyclic frequency α = α0. Since the AWGN is awide sense stationary process and does not possess second-order cyclostationarity, it will not have a peak at any cyclicfrequency. On the other hand, the band-pass BPSK signalexhibits second-order cycle frequencies at α0/2 = fc + m/T0

[2, 9], for some integer m. Since the strongest spectral lines ofa BPSK signal appear at= fc, the strongest cyclic components


are observed at α0/2 = fc [9]. Therefore, the local decisionvariable for cyclostationary detection from jth CR user ischosen to be the value of the SCD in (7) evaluated at k = 0.This value is used as the jth element in the feature vectord = [d1 · · ·dN ]T that will be presented to the classifier in theclassification stage, where dj = Sα0

r j[k] with k = 0.

3.3. Coherent Based Feature Extraction. Another sensingscheme investigated in this work is feature extraction usingcoherent detection. Coherent detection is performed bydemodulating the primary user’s signal, which requires apriori information of the primary signal such as packetformat, control, or synchronization sequences. [6]. If thesynchronizing preamble patterns are known at the CRnetwork end, coherent sensing can be exploited by corre-lating the incoming signal with the known patterns. This iseffectively correlating the signal with itself resulting in anautocorrelation function that peaks at zero delay when theprimary user is present. Primary users are assumed to use aframe size of M bits with an L-bit synchronization preamblereferred to as xp[n]. Accordingly, the cognitive users will beacquiring data during the preamble period (i.e., L bits everyM bits). The received signal from jth CR user, r j(t), is cross-correlated with the preamble sequence over the preamblelength to obtain

Rjc[k] =

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

∣∣∣gj∣∣∣2L∑

n=1

∣∣∣xp[n]∣∣∣2

+ Re

⎧⎨⎩

L∑n=1

xp[n]η∗j [n]

⎫⎬⎭ : H1

Re

⎧⎨⎩

L∑n=1

xp[n]η∗j [n]

⎫⎬⎭ H0.

(8)

Under hypothesis H1, Rjc[k] becomes an autocorrelation ofthe transmitted preamble having a strong peak at k = 0.However, under H0, Rjc[k] will not exhibit strong peaks. Thepeak value of Rjc[k] is used as the jth element in the feature

vector d = [d1 · · ·dN ]T that will be presented to the classifierin the classification stage, where dj = max{|Rjc[k]|}.

4. Polynomial Classifiers

In this paper, we use polynomial classifiers (PCs) as theclassification models to decide on the spectrum availability.Polynomial classifiers have shown improved recognition per-formance with lower computational complexity as comparedto other recognitions methods, such as neural networks andhidden Markov models [25, 29]. Furthermore, polynomialclassifiers deal with simple mathematical operations such asmultiplication and summation, which makes them suitablefor practical implementation in digital signal processingalgorithms. The principle of a polynomial classifier is theexpansion of the input feature space into a higher dimen-sional space that is linearly separable [30].

Consider an input pattern d = [d1 · · ·dN ]T , where Nis the number of features and T represents the transposeoperation. The rth order polynomial classifier first performsa vectorial mapping of the N-dimensional feature vector, d,

into an l-dimensional vector ϕ(d). The elements of ϕ(d) aremonomials of the form [24, 25]

ϕ(d) =[

1,d1,d2, . . . dN ,d21,d1d2,d1d3, . . . ,d1dN ,d3

1,d21d2,

. . . d21dN , . . . ,dr1,dr1d2, . . . dr1dN ,

d22,d2d3, . . . ,d2dN ,d3

2,d22d1,d2

2d3, . . . d22dN ,

. . . ,dr2,dr2d1, . . . ,dr2dN , . . .]T.

(9)

Then, the output scorer yi is obtained at the output layer afterlinearly combining the expansion terms ϕ(d) using

yi = wTi ϕ(d), (10)

where wi is the model (weights) of class i. The dimensionalityof the expanded vector ϕ(d) can be expressed in terms ofthe polynomial order and the dimensionality of the inputvector d. The design of the classifier comprises of two stages,namely, training and testing.

4.1. Training. The training process involves finding theoptimal model parameters that best map a multidimensionalinput sequence to a corresponding one-dimensional targetsequence. The model is designed to classify between two dif-ferent classes, Hi for i = {0, 1}, corresponding to the binaryhypotheses in (1). The multidimensional input sequenceDtrain is a K × N matrix, where N is the dimensionality ofthe input feature vectors (provided by N CR users) and K isthe number of feature vectors used in the training process.The training matrix Dtrain is given by

Dtrain =

⎡⎢⎢⎣d11 d12 · · · d1N

.... . .

...dK1 dK2 · · · dKN

⎤⎥⎥⎦. (11)

The one-dimensional target vector ti = [ti1 ti2 · · · tiK ]T fori = {0, 1} consists of K elements where tiz = 1 if thecorresponding zth feature vector belongs to class i, and tiz =0 if the corresponding zth feature vector does not belong toclass i, for z = 1, 2, . . . ,K .

The training vectors are expanded into their polynomialterms as defined in (9) resulting in a model training M dataset of size (K × l) that is defined by

M =[ϕ(d1) ϕ(d2) · · · ϕ(dK )

]T. (12)

Once training feature vectors are expanded into theirpolynomial basis terms, the polynomial classifier is trainedto find an optimum set of weights, w

opti , that minimizes

the Euclidian distance between the ideal target vector ti andthe corresponding outputs of the classifier using the mean-squared error criterion to get

wopti = arg

w{min‖Mw − ti‖2}. (13)


The problem of (13) can be solved using the method ofnormal equation to explicitly obtain the optimal model forthe two-class spectrum sensing problem as [25, 29]

wopti =

(MTM

)−1MT ti. (14)

4.2. Testing. In the testing stage, novel feature vectors dtest areused to represent the testing data set. The features are initiallyexpanded into their basis termsϕ(dtest) and then presented tothe trained models {w

opt0 , w

opt1 } to obtain the corresponding

set of scores {yi} as

{yi} = ϕ(dtest) w

opti for i = 0, 1. (15)

Accordingly, we assign the testing feature vector to hypothe-sis Hi that satisfies [25]

Yd = argi

{max

{yi}}. (16)

Ideally, the output from the classifier model, for a certaininput feature vector, should be one when the spectrum isoccupied and zero when the spectrum is idle as we apply itto the corresponding model w

opti . However, when new input

data are fed to the classifier, the output has values varyingaround one for hypothesis H1 and values varying aroundzero for H0 and vice versa. In order to achieve a desired levelof constant false alarm rate, a threshold needs to be definedto separate the two classes instead of just comparing differentmodels output scores.

An iterative algorithm is applied at the training stageto search for the threshold for different signal levels thatachieves a specific false alarm rate as follows. First, the outputscore is computed by subjecting a validation data set (withknown class labels) to the model w

opt1 . The threshold is

initialized to λ = 0.5, such that the global decision variableYd = 1 if y1 > λ and Yd = 0 otherwise. The false alarmrate is then estimated by comparing the output decisionsof all validation feature vectors to the ideal output t1. Afalse alarm will be declared when the output decision is oneindicating that the spectrum is busy while the ideal outputt1 is zero indicating that the actual spectrum is available.The threshold λ is incremented or decremented with a smallvalue such that the desired false alarm rate is achieved witha specified accuracy, for example, a mean-squared error ofless than 1%. The above steps are repeated for the validationdata with different received SNR levels to form a lookuptable that could be used when new test data is received.Note that the threshold setting operation, in addition tothe training process, is performed offline. The training andvalidation data sequences are retrieved from a database thatis maintained at the CRBS for offline training and validation.

5. Simulation Results

In this section, the performance of a first-order polynomialclassifier (known also as linear classifier (LC)) and second-order polynomial classifiers (PCs) using the previously dis-cussed feature extraction methods is evaluated. A band pass

BPSK primary signal is used when cyclostationary featuredetection is utilized, while antipodal baseband signaling withS(k) = ±1 in the case of coherent detection. To emulatea more challenging and practical situation, we assumethe distance between the CR network and the primarytransmitter is relatively large; hence, the average receivedSNRavg is in the low SNR range, that is, SNRavg ≤ 0 dB.In addition, the jth CR receives a signal with a signal-to-noise ratio SNR j that depends on the ith CR’s proximityfrom the primary user. To account for signal shadowing,SNR j follows a log-normal distribution with a varianceσ2 = 4 dB and a mean equivalent to SNRavg . The small-scale channel variations follow a flat Rayleigh fading model.It is also assumed that the channel variation is relativelyslow compared to the bit duration (slow fading model).We remark that the simulation parameters were used forillustrative purposes, and other values could be used withoutloss of generality.

5.1. Energy-Based Feature Extraction. Energy detection isperformed at the various secondary users, and the extracteddecision variables are provided to the recognition model atthe CRBS. The probability of detection achieved by the LCand PC at different average received signals levels is presentedin Figure 4. The results are obtained for a window size of200 bits and a target false alarm (Pf ) of 10%. The value ofthe false alarm rate was chosen to be consistent with the IEEE802.22 requirements for CR networks [3]. It is interestingto notice that although the PC requires more memoryand computational complexity to perform the expansionoperation, it does not improve the detection probabilityperformance compared to the LC. Hence, it is recommendedto use an LC since it provides good performance with lessrequired memory space and computational cost resultingin making faster decisions about the availability of thespectrum. Moreover, the advantage of cooperative sensingcompared to single-radio-based sensing is demonstrated bythe improvement in the detection performance as the num-ber of secondary users contributing to signal classificationis increased. For instance, a received SNR of around −9 dBis appropriate to reach a detection probability of 90% withthree CRs, while a received signal with an average SNR ofaround −6.5 dB is required to achieve the same detectionrate with one CR, resulting in a 2.5 dB gain which improvesthe ability to avoid interfering with weak primary users. It isnotable from Figure 4 that the enhancement in performancediminishes as the number of receivers collaborating in globaldecision increases.

The probability of detection results of the energy detectorfor a received signal with SNRavg = −5 dB, N = 3 users, andPf = 10% is depicted in Figure 5 for both the LC and PC asa function of the observation window size. It is evident thatthe detection performance is highly affected by the windowsize over which the local decision variables are estimated.As the window size increases, the data used for training andtesting becomes more representative to the present signal inthe spectrum, and hence the classifier’s output score is moreaccurate. However, the larger the window size is, the longer


00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Average received SNR (dB)

Det

ecti

on p

roba

bilit

y

−20 −18 −16 −14 −12 −10 −8 −6 −4 −2

LC, N = 1, energyLC, N = 3, energyLC, N = 5, energy

2nd-order PC, N = 3, energy2nd-order PC, N = 5, energy

Figure 4: Detection performance for cooperative LC and PC with energy-based feature extraction.

20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Observation window size M (bits)

Det

ecti

on p

roba

bilit

y

LC, energy2nd-order PC, energy

Figure 5: Impact of the window size on detection performance of energy-based schemes: SNRavg = −5 dB, N = 3 users, and Pf = 10%.

it takes for decision making of spectrum availability by theclassifier at the base station. This yields a delay in spectralallocation when the spectrum is available, hence, resulting inlower spectral utilization.

A useful performance measure is the receiver operationalcharacteristic (ROC) that represents the variation of theprobability of detection with the false alarm probability atcertain operational parameters. Since the LC provided abetter choice with energy detection, its ROC is obtainedas shown in Figure 6 when the primary signal is receivedat an SNRavg = −14 dB and observation window size ofM = 200 bits. It is observed that the detection probabilitydeteriorates for low false alarm rates and improves whenhigher false alarm probability is tolerable. This behavioris expected since in order to achieve a low false alarmrate, the threshold level needs to be raised. Raising the

threshold level above classifier’s output score, correspondingto occupied spectrum class, may lead to miss detectingprimary signal’s presence, and consequently causing moreinterference to the primary network’s users. It can be notedthat higher detection is accomplished with higher number ofcooperating CRs.

5.2. Cyclostationary Based Feature Extraction. Simulationresults for the proposed classification system when cyclosta-tionary features are fed to the CRBS for spectrum sensing arepresented in Figure 7. It is shown that cyclostationary featuredetection can achieve very high detection probability evenwith low SNR values by using more cooperating CRs. Forinstance, a detection probability of about 90% is achievedwith an average SNR of −18 dB when five CRs are used.


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Figure 6: ROC curves of energy-based linear classifier scheme: SNRavg = −14 dB and M = 200 bits.

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−20 −18 −16 −14 −12 −10 −8 −6 −4 −2

LC, N = 1, CFDLC, N = 3, CFDLC, N = 5, CFD

2nd-order PC, N = 3, CFD2nd-order PC, N = 5, CFD

Figure 7: Detection performance for cooperative LC and PC with cyclostationary-based feature extraction: Pf = 10% and M = 200 bits.

The results demonstrate improved performance comparedto the energy-based detector. For instance, a gain of about4 dB is observed when the number of CRs cooperating inmaking the decision increases from one to three at Pd = 90%.As in the case of energy detection, it is observed that thereis no significant performance improvement as the order ofthe classifier is increased from first order to second order.Furthermore, performance improvements due to increasingcooperative CRs saturate for higher number of users.

The detection performance of the cyclostationary detec-tion scheme is improved by increasing the observationwindow size as illustrated in Figure 8. The detection results

for the LC and PC are presented at SNRavg = −14 dB, N = 3users, and Pf = 10%. Increasing the observation window sizefrom 20 to 200 bits results in improving the probability ofdetecting from about 70% to 98%, at a SNRavg of −14 dB.The ROC curve is shown in Figure 9 for a SNRavg =−14 dB and observation window of 200 bits indicating thatusing more cooperating radios results in better detectionperformance.

5.3. Coherent-Based Feature Extraction. For the coherent-based scheme, Figure 10 shows the detection probabilityas the received primary signal’s level is varied. Coherent


20 40 60 80 100 120 140 160 180 2000

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Figure 8: Impact of the window size on detection performance of cyclostationary-based schemes: SNRavg = −14 dB, N = 3 users, and Pf =10%.

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Figure 9: ROC curves of cyclostationary-based linear classifier scheme: SNRavg = −14 dB and M = 200 bits.

detection was simulated for a primary signal with a preamblesize of L = 16 bits and a frame length of M = 200 bits. It isnoticed that a gain of about 6 dB is achieved as the numberof collaborating radios N increases from one to three, at adetection probability of 90%. The achieved gain, however,reduces to around 1.5 dB as N increases from three to five.Coherent detection provides reliable signal identificationwith Pd > 98%, when the received signal level is above−10 dB and N = 5. We notice that the LC and PC performcomparably when coherent detection is utilized in featureextraction.

The ROC curve for coherent-detection-based sensingfor various numbers of cooperative CRs is demonstrated inFigure 11. It is apparent that there is a performance variationas the different number of CRs collaborates in making the

decision. The performance gap between various numbers ofCRs shrinks as the false alarm probability increases.

Finally, Figure 12 shows the performance gain achievedusing coherent detection LC scheme as the length ofpreamble sequence increases. The figure presents the SNRavg

required to obtain a specific detection probability andfalse alarm rate, as the preamble length increases. Longerpreamble sequences result in lower values of the requiredSNRavg indicating that a lower level of received primarysignal is sufficient to achieve a certain detection rate aspreamble length is increased.

5.4. Discussion. Among the three considered schemes, cyclo-stationary feature detection provides the best performance


LC, N = 1, CDLC, N = 3, CDLC, N = 5, CD

2nd-order PC, N = 3, CD2nd-order PC, N = 5, CD

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0−20 −18 −16 −14 −12 −10 −8 −6 −4 −2

Average received (SNRavg) (dB)

Figure 10: Detection performance for cooperative LC and PC with coherent-based feature extraction: Pf = 10% and preamble lengthL = 16 bits.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

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Figure 11: ROC curves of coherent-based linear classifier scheme: SNRavg = −14 dB and L = 16 bits.

in terms of both detection and false alarm rates, whileenergy detection results in the poorest performer. Theimplementation of cyclostationary feature detection relies onthe knowledge of carrier frequency and modulation type ofthe primary signal. The obvious drawback of cyclostationarydetection is the high computational complexity requiredto extract cyclic features at CRs, as compared to othertechniques. On the other hand, it provides high reliability tothe CR network under low SNR conditions.

It has been shown that a longer sensing time canimprove the detection performance considerably. However,detection improvement due to increasing sensing time isachieved at the expense of lowering the network’s agility,since longer time is required to decide on the vacancy of thespectrum. This comment is very important when comparing

the performance of the cyclostationary scheme over coher-ent scheme. Specifically, the cyclostationary-based schemeachieves a better detection performance when comparedto the coherent detection scheme. This is so because theformer uses the entire frame in the process of decisionmaking. On the other hand, the coherent-based scheme usesa shorter observation window (preamble) leading to a moretimely decision making. Increasing the preamble length willimprove the performance for the coherent-based scheme butat the expense of a reduction in the spectral efficiency of theprimary user, while the cyclostationary-based scheme doesnot suffer from this drawback.

Finally, although energy detection represents the featureextraction scheme with least detection capability under lowSNR conditions, representing severe fading and shadowing,


20 30 40 50 60 70 80

Preamble length L (bit)

P f = 10%, Pd = 90%P f = 10%, Pd = 80%

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dB)

Figure 12: Impact of the preamble length on detection performance of coherent-based linear classifier scheme.

it is still an attractive technique under high SNR regimesdue to its simplicity and minimum prior informationrequirements.

6. Conclusion

In this paper, pattern recognition models were proposed totackle the problem of spectrum sensing in CR networks. Theproposed classifier model is based on collaborative sensing,in which secondary users monitor channel usage in a givenarea and cooperate through a centralized node to provide thespectrum occupancy information. The cooperation betweensecondary users was achieved through first- and second-order polynomial classifiers that were modeled, trained,validated, and evaluated. Results indicate that both the linearand the polynomial classifiers provide high detection ratesof primary signal over wireless fading channel and verysmall signal to noise ratios. Moreover, simulation resultsshow that both classifiers perform comparably; consequently,the linear classifier is chosen as the best model for coop-erative CR networks due to its lower complexity. Energy-, cyclostationary-, and coherent-based feature extractiontechniques were compared. Simulation results demonstratedthat cyclostationary detection constitutes the best candidatefor feature extraction when information on primary signal isavailable, since it outperforms energy and coherent detectionsubstantially. However, the remarkable detection capabilityof cyclostationary detection is achieved at the expense ofhigher implementation complexity.

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